Ordered mechanism simple, initial rate equations

The initial rate equation is again of the form of Eq. (1) with the kinetic coefficients as in Table I, which shows that the mechanism differs from the simple ordered mechanism in three important respects. First, the isomerization steps are potentially rate-limiting evidence for such a rate-limiting step not attributable to product dissociation or the hydride-transfer step (fc) has been put forward for pig heart lactate dehydrogenase 25). Second, Eqs. (5) and (6) no longer apply in each case the function of kinetic coefficients will be smaller than the individual velocity constant (Table I). Third, because < ab/ a< b is smaller than it may also be smaller than the maximum specific rate of the reverse reaction that is, one of the maximum rate relations in Eq. (7) need not hold 26). This mechanism was in fact first suggested to account for anomalous maximum rate relations obtained with dehydrogenases for which there was other evidence for an ordered mechanism 27-29). 

The rates of product formation (and reactant consumption) are seen to be of order one half in the initiator or, if the reaction is initiated by a reactant converted in the propagation cycle, the rate equation involves exponents of one half or integer multiples of one half. For an example, see the hydrogen-bromide reaction below. This is one of the exceptions to the rule that reasonably simple mechanisms do not yield rate equations with fractional exponents. [The other exceptions are reactions with fast pre-dissociation (see Section 5.6) and of heterogeneous catalysis with a reactant that dissociates upon adsorption.]... 

Mechanisms for most chemical processes involve two or more elementary reactions. Our goal is to determine concentrations of reactants, intermediates, and products as a function of time. In order to do this, we must know the rate constants for all pertinent elementary reactions. The principle of mass action is used to write differential equations expressing rates of change for each chemical involved in the process. These differential equations are then integrated with the help of stoichiometric relationships and an appropriate set of boundary conditions (e.g., initial concentrations). For simple cases, analytical solutions are readily obtained. Complex sets of elementary reactions may require numerical solutions. 

Analysis of Cure. A simple analysis of the cure results for short term steady flow can be performed by noting that for a number of polymerization reactions, the early stages of cure can be described by a first order type equation (9,10). In the simplest case this would mean that log (n) would vary linearly with time. To examine this possibility the data for various shear rates were analyzed by plotting log (n) vs. time (Figures 13 and 14). If the Initial points (zero cure time data) are excluded, the data for each shear rate can be fit, to a first approximation, with a straight line. The fact that the zero cure time points do not fall near the lines suggests that the mechanical property results show an Initiation time Just as was found previously In thermal experiments (2). 

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